Transferring a non-wordpress database

Hey all! I’m working on a redesign for a client. She’s been using a custom-made php system for several years but I’m building a new WordPress site for her. The only problem is, she doesn’t want to copy and paste all the many years of posts and images that she’s written over to the new site. Is there a way to transfer the old database to the new wordpress system?

The old site is here: https://meadowhaven.net/
The wordpress redesign is here (will be moved when finished):https://www.kreationart.com/client/test/meadowhaven/

Thank you!